APPLIED ANALYSIS (3RD ED‪)‬

This book is to be a new edition of Applied Analysis. Several fundamental materials of applied and theoretical sciences are added, which are needed by the current society, as well as recent developments in pure and applied mathematics. New materials in the basic level are the mathematical modelling using ODEs in applied sciences, elements in Riemann geometry in accordance with tensor analysis used in continuum mechanics, combining engineering and modern mathematics, detailed description of optimization, and real analysis used in the recent study of PDEs. Those in the advance level are the integration of ODEs, inverse Strum Liouville problems, interface vanishing of the Maxwell system, method of gradient inequality, diffusion geometry, mathematical oncology. Several descriptions on the analysis of Smoluchowski-Poisson equation in two space dimension are corrected and extended, to ensure quantized blowup mechanism of this model, particularly, the residual vanishing both in blowup solution in finite time with possible collision of sub-collapses and blowup solutions in infinite time without it.

Contents:
Mathematical ModelingField FormationObjects and CoordinatesLanguages of Modern GeometryOptimizationsCalculus of VariationInfinite-Dimensional AnalysisScatteringRandom Motion of ParticlesLinear PDEReal Analysis in PDENonlinear PDEAppendix A: Catalogue of Mathematical AnalysiAppendix B: An Elliptic-Parabolic SystemAppendix C: Commentaries
Readership: Undergraduate students studying mathematics, physics, chemistry, engineering; graduate students specialized in mathematical analysis, real analysis, theory of partial differential equations; researches and specialists in the theory of nonlinear partial differential equations.

Review of the First Edition:'One good feature of the book is the rather large bibliography of mostly research papers that pertain to the applications mentioned in the textual material. This feature should be a huge help in understanding the ideas and concepts presented and soften some of the abstractions … most topics are covered in an introductory way and serve to tie together this body of mathematical methods that can serve the natural sciences.' - Mathematical Reviews

Key Features: Comprehensive coverage of the topics Added and updated materials in accordance with recent developments in natural sciences and mathematics New materials added here are useful to access modern applications of mathematics in digitalization, artificial intelligence, and data science, developed by the fundamental notions described in the former edition